![]() ![]() The rows of the table corresponding toô= 80 andô= 100ûwe see thatö(80ûø)increases at a relatively constant rate ofĪpproximately 1 ◦Fper10%relative humidity, whileö(100ûø)increases more quickly (at ûrst with an average rate ofĬhange of 5 ◦Fper10%relative humidity) and at an increasing rate (approximately 12 ◦Fper10%relative humidity forģ. Variable that gives the humidex values for different relative humiditieswhen the actual temperature is 100 ◦F. (d)ĉ=ö(80ûø)means thatôis ûxed at 80 andøisallowedtovary,resultinginafunctionoføthat gives the humidex valuesįor different relative humidities when the actual temperature is 80 ◦F. ![]() (c) Looking at the column corresponding toø= 50 ,weseethatö(ôû50) = 88whenô= 85. (b) Looking at the row corresponding toô= 90 ,weseethatö(90ûø) = 100 whenø= 60. The perceived air temperature is approximately 124 ◦F. (a) From Table 3,ö(95û70) = 124, which means that when the actual temperature is 95 ◦Fand the relative humidity is70%, Table 1 (look at the column corresponding toö= 50 ), the function increases almost linearly asôincreases.Ģ. Other words, the function gives wind-chill index values for different temperatures when the wind speed is 50 kmýh (e) The function÷=ö(ôû50)means that we ûxöat 50 and allowôto vary, again giving a function of one variable. Table 1 (look at the row corresponding toô=− 5 ), the function decreases and appears to approach a constant value asö Other words, the function gives wind-chill index values for different wind speeds when the temperature is− 5 ◦C (d) The function÷=ö(− 5 ûö)means that we ûxôat− 5 and allowöto vary, resulting in a function of one variable. (c) The question is asking: when the wind speed is 20 kmýh, what temperature gives a wind-chill index of− 49 ◦C?From ![]() (b) The question is asking: when the temperature is− 20 ◦C, what wind speed gives a wind-chill index of− 30 ◦C?From (a) From Table 1,ö(− 15 û40) =− 27, which means that if the temperature is− 15 ◦Cand the wind speed is 40 kmýh, then theĪir would feel equivalent to approximately− 27 ◦Cwithout wind. 14 PARTIAL DERIVATIVES 14 Functions of Several Variablesġ. ![]()
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